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Monodromy of Hyperelliptic Abelian Integrals

Part of the Advanced Courses in Mathematics CRM Barcelona book series (ACMBIRK)

Abstract

We want to show that in the case of Hamiltonians of the form
$$ H(x,y) = y^2 + f(x), $$
where f(x) is a polynomial of degree n, the existence of a tangential center implies that either P dx — Qdy is relatively exact, or the polynomial f(x) is composite. That is, it can be expressed as a polynomial of a polynomial, f(x) = a(b(x)), in a non-trivial way.

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Copyright information

© Birkhäuser Verlag 2007

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